A262935 Increasing distances of lonely twin primes pairs to nearest prime.

1, 2, 4, 6, 10, 12, 16, 18, 28, 30, 34, 42, 46, 48, 58, 88, 90, 94, 124, 130, 136, 154, 162, 168, 172, 178, 202, 216, 258, 264, 294, 342, 352, 354, 364, 366, 370, 378, 396, 408

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Formula

a(n) = d if ( (p(i+1) = p(i)+2) AND (d = min(p(i+2)-p(i+1), p(i)-p(i-1)) > a(n-1)) ), where a(0) = 0, p(k) = prime(k) = A000040(k).

Example

(3,5) is a twin primes pair, min(7-5, 3-2)=1, therefore a(1)=1.
(5,7) is a twin primes pair, min(11-7, 5-3)=2>1, therefore a(2)=2.
(11,13) is a twin primes pair, min(17-13, 11-7)=4>2, therefore a(3)=4.

Prog

(PARI) {m=0; q=5; s=3; t=2; forprime(p=6, 10^9, if((q-s==2) && (min(p-q, s-t)>m), m=min(p-q, s-t); print1(m, ", ") ); t=s; s=q; q=p; )}

Crossrefs

Cf. A035789, A069453, A069455, A262936.

Sequence in context: A358816 A127965 A117891 * A178539 A072752 A036634

Adjacent sequences: A262932 A262933 A262934 * A262936 A262937 A262938

Keyword

nonn

Author

Dmitry Petukhov, Oct 04 2015

Status

approved